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Simplifying 4b2 + -1b + -200 = 0 Reorder the terms: -200 + -1b + 4b2 = 0 Solving -200 + -1b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -50 + -0.25b + b2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.25b + 50 + b2 = 0 + 50 Reorder the terms: -50 + 50 + -0.25b + b2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.25b + b2 = 0 + 50 -0.25b + b2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.25b + b2 = 50 The b term is -0.25b. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25b + 0.015625 + b2 = 50 + 0.015625 Reorder the terms: 0.015625 + -0.25b + b2 = 50 + 0.015625 Combine like terms: 50 + 0.015625 = 50.015625 0.015625 + -0.25b + b2 = 50.015625 Factor a perfect square on the left side: (b + -0.125)(b + -0.125) = 50.015625 Calculate the square root of the right side: 7.07217258 Break this problem into two subproblems by setting (b + -0.125) equal to 7.07217258 and -7.07217258.Subproblem 1
b + -0.125 = 7.07217258 Simplifying b + -0.125 = 7.07217258 Reorder the terms: -0.125 + b = 7.07217258 Solving -0.125 + b = 7.07217258 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = 7.07217258 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = 7.07217258 + 0.125 b = 7.07217258 + 0.125 Combine like terms: 7.07217258 + 0.125 = 7.19717258 b = 7.19717258 Simplifying b = 7.19717258Subproblem 2
b + -0.125 = -7.07217258 Simplifying b + -0.125 = -7.07217258 Reorder the terms: -0.125 + b = -7.07217258 Solving -0.125 + b = -7.07217258 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = -7.07217258 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = -7.07217258 + 0.125 b = -7.07217258 + 0.125 Combine like terms: -7.07217258 + 0.125 = -6.94717258 b = -6.94717258 Simplifying b = -6.94717258Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.19717258, -6.94717258}
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